What is the optimal time complexity of solving Arrays are disjoint or not?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Arrays are disjoint or not?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Arrays are disjoint or not?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Arrays are disjoint or not?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Arrays are disjoint or not

Learn how to solve the 'Arrays are disjoint or not' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Write a function are_disjoint(arr1, arr2) that takes two lists of integers and returns True if they have no elements in common (disjoint), and False otherwise.

Constraints

•0 <= len(arr1), len(arr2) <= 10^5
•-10^6 <= arr1[i], arr2[i] <= 10^6

Examples

Example 1

Input

arr1 = [1, 2, 3], arr2 = [4, 5, 6]

Output

True

Explanation

No element appears in both arrays.

Example 2

Input

arr1 = [1, 2, 3], arr2 = [3, 4, 5]

Output

False

Explanation

3 is present in both arrays.

Example 3

Input

arr1 = [], arr2 = [1, 2, 3]

Output

True

Explanation

An empty array is disjoint with any array.

Need a Hint?

Use simple arithmetic operators (like modulo `%`, division `//`), conditional checks, or loops to inspect number properties.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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